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ss7ja [257]
3 years ago
10

Which are solutions of x2=-11+4?

Mathematics
2 answers:
saul85 [17]3 years ago
7 0

ANSWER

x =  - \sqrt{ 7}i \:  \: or \:  \: x =  + \sqrt{ 7}i

EXPLANATION

The given expression is

{x}^{2}  = - 11 + 4

Simplify the left hand side to get:

{x}^{2}  =  - 7

Take square root

x = \pm  \sqrt{ - 7}

x =  \pm \sqrt{ 7}  \times  \sqrt{ - 1}

Note that:

{i}^{2}  = -  1 \implies \sqrt{ - 1}  = i

x =  \pm \sqrt{ 7}i

Split the plus or minus sign

x =  - \sqrt{ 7}i \:  \: or \:  \: x =  + \sqrt{ 7}i

Dovator [93]3 years ago
3 0

For this case we have a quadratic equation of the form:

ax ^ 2 + bx + c = 0\\x ^ 2 + 11x-4 = 0

Where:

a = 1\\b = 11\\c = -4

We find the roots:

x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}\\x = \frac {-11 \pm \sqrt {11 ^ 2-4 (1) (- 4)}} {2 (1)}\\x = \frac {-11 \pm \sqrt {121 + 16}} {2}\\x = \frac {-11 \pm \sqrt {137}} {2}

The roots are:

x_ {1} = \frac {-11+ \sqrt {137}} {2}\\x_ {2} = \frac {-11- \sqrt {137}} {2}

Answer:

x_ {1} = \frac {-11+ \sqrt {137}} {2}\\x_ {2} = \frac {-11- \sqrt {137}} {2}

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